In order to determine the relative position of a mobile in relation to a reference station, satellite-based position-measuring means are currently used, employing, for example, radio signals transmitted by GPS (Global Positioning System) or other similar systems (GLONASS system, future GALILEO system) satellites.
In the GPS system, the signal transmitted by a satellite is coded and the time taken by the signal to reach the point to be located is used to determine the distance between this satellite and this point, preferably referred to as the pseudo-range to take account of synchronization errors between the satellite clock and the station clock. These synchronization errors are conventionally eliminated through calculation when signals are received from at least four different satellites. Determination of the distance between the point to be located and a plurality of satellites, with knowledge of the geographic coordinates of the satellites, enables calculation of the coordinates of the point to be located, most often coordinates expressed as latitude, longitude and altitude at a fixed terrestrial reference point.
In order to determine the relative position of a mobile in relation to a reference station, a method known as “differential GPS” is used, which involves locating a point in relation to a reference station and not in relation to an independent terrestrial reference point: by providing a receiver at the reference station, it is possible to determine the relative position of the mobile in relation to the reference station using measurements taken at the station and at the mobile.
The advantage of this method is that it enables to increase the positioning precision. In fact, the measurement distortions linked to the random characteristics of radio satellite signal propagation are most often strongly correlated in space, and precise knowledge of the position of the reference station allows these to be largely compensated by comparing measurements taken at the station at theoretical distances.
Propagation time is determined on the one hand with reference to a reference time of the pseudo-random code which modulates a carrier frequency transmitted by the satellite, this code reference time enabling in particular the approximate position of the mobile to be determined, i.e. accurate to within several meters to several tens of meters: the propagation time is determined on the other hand with reference to the phase of the received carrier, the phase measurement, which is less noisy than the code measurement, enabling the position of the mobile to be determined with greater precision, i.e. accurate to within centimeters, but being dependent on elimination of the ambiguity surrounding the number of phase rotations, since the phase can only be known a priori to within 2π, where 2π corresponds to a distance equal to the wavelength of the radio frequency signal transmitted by the satellites.
Attention will be focused below on phase measurements only, since code position measurements can be performed in a conventional manner. The pseudo-ranges supplied by the GPS receiver of the mobile or the reference station will therefore be considered essentially as numerical phase values, a phase value being directly converted into a distance value, with knowledge of the wavelength of the radio signal transmitted by the satellites.
The central point of centimetric positioning techniques using phase measurements is the preliminary calculation, referred to as “initialization”, in which the problem of ambiguities surrounding the number of wavelengths is resolved. This calculation conventionally requires prior knowledge of an estimated position of the mobile, which may be obtained in particular using a method such as that described in patents FR 2 715 230 and FR 2 764 708. This estimated position is then re-aligned with the precise position, then validated during this initialization calculation.
Particular consideration will then be given to the stage in which the estimated position is realigned towards a precise position.
The quality of this precise position depends in particular on the distance between the mobile and the reference station.
In fact, flaws in the differential method initially arise due to the fact that radio satellite signals do not encounter exactly the same propagation conditions on the satellite-station and satellite-mobile paths. The differences in the conditions encountered, which are more or less zero in the immediate vicinity of the station, naturally increase with distance.
This difference is mainly due to the ionosphere which is crossed by satellite-station and satellite-mobile signals at different points, given that the ionosphere is not a homogeneous medium. The differential measurements based on the propagation times of the satellite-station and satellite-mobile signals are therefore adversely affected by this difference. This difference may result in an error in the position of the mobile in relation to the reference station ranging from 1 to several cm per km of distance. Thus, for a distance between the station and the mobile which is greater than a distance in the order of 10 km, the position of the mobile in relation to the reference station cannot be guaranteed with centimetric precision.
A first solution described in FR 2764708 A1 proposes, on the one hand, to reduce the initialization calculation time, in particular the time for calculating an approximate unambiguous position using, in particular, linear combinations of transmission frequencies L1 and L2 of GPS system satellites. On the other hand, it proposes to reduce the ionospheric error; the reduction in the ionospheric error applies during the realignment phase. It consists in calculating, on the basis of the approximate unambiguous position, on the one hand, a position (XL1, YL1, ZL1) for L1 and, on the other hand, a position (XL2, YL2, ZL2) for L2, the precise position (X, Y, Z) then resulting from the following linear combination: X=(1.65 XL1−XL2)/0.65 Y=(1.65 YL1−YL2)/0.65 Z=(1.65 ZL1−ZL2)/0.65.
However, due to the calculation of a position on L1, adversely affected by an ionospheric error E, and the calculation of the position on L2, adversely affected by an ionospheric error 1.65*E, it is still not possible to eliminate ambiguities if the ionospheric error increases, which occurs when the distance between the mobile and the reference station increases.
A different solution conventionally proposed consists in providing not one but a plurality of reference stations, constituting what is commonly referred to as a “network”. According to this technique, it is possible to know not only the errors measured at one point, as is done in the case of “differential GPS”, but also their gradient of evolution in the zone. The effect of spatial decorrelations of the errors is therefore largely compensated. This solution is effective, but is of course laborious and costly to implement due to the infrastructure which it requires and the cost of the communications between the stations and the mobile. Furthermore, such an infrastructure will not exist everywhere.
A method based on exploitation of the fact that the ionospheric error is a function of frequency (1/f2 in the first approximation) has also been proposed.
It is then possible to determine this error or to reduce or even eliminate it by replacing the frequency f (designated by L1 or L2 in the case of the GPS system) in the calculations with a linear combination of the carrier frequencies of the signals transmitted by the satellites, i.e. by a linear combination of L1 and L2.
The result of a linear combination of L1, L2 is a new frequency L3 to which a wavelength referred to as the apparent wavelength corresponds.
For example, in the case of the GPS system in which L1=1.57542 GHz (corresponding to a wavelength of around 19 cm) and L2=1.22760 GHz (corresponding to a wavelength of around 24 cm), the combination of frequencies referred to as “Iono-Free”, 9L1−7L2 allows the ionospheric error to be almost completely eliminated. The corresponding apparent wavelength is 5 cm.
However, this method is very difficult to apply due to the great difficulty in eliminating the ambiguities surrounding such short wavelengths.